Generalizes Dolbeault cohomology computation to Levi-flat CR structures on compact Lie groups.
problem Computing Dolbeault cohomology for Levi-flat CR structures on compact Lie groups.
method Algebraic classification of left-invariant CR structures combined with Pittie's result on compact Lie groups.
result Generalization of Dolbeault cohomology computation to Levi-flat CR structures.
An almost para-CR structure on a manifold M is given by a distribution HM⊂TM together with a field K∈Γ(End(HM)) of involutive endomorphisms of HM. If K satisfies an integrability condition, then (HM,K) is called a para-CR structure. The notion of maximally homogeneous para-CR structure of …
Boundary properties of hyperbolic groups are invariant under a maximization procedure.
problem Proving boundary properties of hierarchically hyperbolic groups are invariant.
method Proving boundary invariance under a maximization procedure.
result Boundary properties of hierarchically hyperbolic groups are invariant under maximization.
Study on almost complex structures with maximal Nijenhuis tensor rank and cohomological properties.
problem Maximally non-integrable almost complex structures and their cohomological properties.
method h-principle and topological invariants characterization.
result Existence of almost complex structures with maximal Nijenhuis tensor rank on parallelizable and certain manifolds.
A characterization of maximal domains of existence of adapted complex structures for Riemannian homogeneous manifolds under certain extensibility assumptions on their geodesic flow is given. This is applied to generalized Heisenberg groups and naturally reductive Riemannian homogeneous spaces. As an application it is s…
Researchers found a maximal antipodal set of three elements in a 7x7 sphere space.
problem Determining the maximal antipodal set in the outer 3-symmetric space S7imesS7. method Investigated the polar and maximal antipodal set P for the given 3-symmetric space S7imesS7. result The maximal antipodal set P has three elements. Study shows almost complex structures with certain tensor properties are prevalent.
problem Characterizing almost complex structures with specific tensor properties.
method Analyzes the space of almost complex structures on compact manifolds.
result The space of almost complex structures with rank at least k Nijenhuis tensor is either empty or dense in each component.
We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the scope of maximal representations. We prove that weakly maximal representations are d…
Study on invariant anti-quasi-Sasakian structures on compact manifolds.
problem Existence and classification of invariant anti-quasi-Sasakian structures of maximal rank.
method Analysis of invariant structures on compact homogeneous Riemannian manifolds and nilpotent Lie groups.
result Classification of invariant anti-quasi-Sasakian structures on nilpotent Lie groups.
The paper explores maximal nilpotent complex structures on Lie algebras.
problem Understanding maximal nilpotent complex structures on Lie algebras.
method Analyzing properties of nilpotent Lie algebras and their complex structures.
result For a nilpotent Lie algebra with step 2, there are only 2-3 maximal complex structures.
We consider complex projective structures on Riemann surfaces and their groups of projective automorphisms. We show that the structures achieving the maximal possible number of projective automorphisms allowed by their genus are precisely the Fuchsian uniformizations of Hurwitz surfaces by hyperbolic metrics. More gene…
Study invariant structures on flag manifolds using transformations and pure spinors.
problem Understanding invariant generalized complex and Kähler structures on flag manifolds.
method Description of moduli spaces using invariant structures, Weyl group action, and pure spinors.
result Alternative description and cell decomposition of moduli spaces.
Study finds maximal symmetry groups for CR structures with specific properties.
problem Determining the maximal dimension of symmetry groups for CR structures.
method Proved the sharp upper bound for the dimension of symmetry groups for homogeneous, 2-nondegenerate CR manifolds.
result The maximal dimension is n2+7 for n≥3. Let S be a closed oriented surface of genus at least 2. Using the parameterisation of the deformation space of globally hyperbolic maximal anti-de Sitter structures on S×R by the cotangent bundle over the Teichmüller space of S, we study the behaviour of these geometric structures along pinching…
Study classifies twist knots with maximal self-linking number in S^3.
problem Classifying transverse-universal knots in S^3.
method Classification of transverse twist knots with maximal self-linking number.
result Obtained an infinite family of non-transverse-universal knots.
Study fibrations of projective spaces for maximal representations.
problem Characterize maximal representations of surface groups.
method Analyze fibrations of projective spaces and use geometric structures.
result Maximal representations correspond to fibrations with specific properties.
Finite groups can be automorphism groups of translation surfaces with poles.
problem Existence of finite automorphism groups on translation surfaces with poles.
method Analyzing translation surfaces with poles and extending results to branched projective structures.
result Finite groups can be automorphism groups of translation surfaces with poles.
New superintegrable systems derived from Frobenius structures.
problem Constructing second-order superintegrable systems.
method Using conification and direct product construction, applying to semi-simple and nilpotent algebras.
result Explicitly constructed second-order superintegrable systems in three dimensions.
New maximal families of compatible Poisson structures derived from geodesically equivalent metrics.
problem Constructing maximal families of compatible Poisson structures.
method Connecting geodesically equivalent metrics and compatible Poisson structures of hydrodynamic type.
result Maximal families of compatible Poisson structures of dimension (n+1)(n+2)/2 are constructed. We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called {\em weakly maximal} representations. We prove that weakly maximal representations are discrete and injective and we describe the structure of the Zariski closure of their image. Furthermore we prove that t…
The paper proposes a method to learn structured representations from unlabeled data using mutual information maximization.
problem Learning structured representations from unlabeled data.
method Adversarial maximization of mutual information between a structured latent variable and a target variable.
result The proposed method outperforms current baselines in document hashing and yields highly compressed interpretable representations.
We classify R-spaces that admit a certain natural Γ-symmetric structure. We further determine the maximal antipodal sets of these structures.
In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally hyperbolic maximal Cauchy-compact anti-de Sitter manifolds in order to define an augmented moduli space. Moreover, we introduce a coordinate system in this space that resembles…
For a 4-manifold represented by a framed knot in S3, it has been well known that the 4-manifold admits a Stein structure if the framing is less than the maximal Thurston-Bennequin number of the knot. In this paper, we prove either the converse of this fact is false or there exists a compact contractible oriented smo…
Compactifies maximal component of surface group representations into a closed ball.
problem Compactifying maximal component of surface group representations.
method Using cores of trees to study dynamics of mapping class group action.
result Boundary points geometrically described as mixed structures.
The study characterizes real flag manifolds with invariant generalized almost complex structures.
problem Characterizing real flag manifolds with invariant generalized almost complex structures.
method Characterization through invariant B-transformations and classification of structures. result No GM2-maximal real flag manifolds admit integrable invariant generalized almost complex structures. Study on CR structures in 7D, proving maximal symmetry dimension.
problem Proving symmetry dimension bound for CR structures in 7D.
method Investigating homogeneous models and proving uniqueness.
result 8 is the maximal symmetry dimension of 3-nondegenerate CR structures in 7D.
Proposes a value-based method for continuous control without an actor.
problem Computational infeasibility of evaluating Q-values in continuous action spaces.
method Structurally maximizable Q-functions, actor-free approach.
result Performance and sample efficiency comparable to actor-critic methods.
We study area-stationary, or maximal, surfaces in the space L(H3) of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. We prove that every holomorphic curve in L(H3) is a maximal surface. We then classify Lagrangian maximal surfa…
Proposes a new method to enhance neural learning by maximizing information gain.
problem Improving neural learning by selecting key variables to maximize information gain.
method Adaptive Ensemble Kalman Filter to quantify uncertainty and maximize information gain.
result The proposed method enables the neural network to learn more effectively from stochastic systems.
Let F be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in Sp(2n,F). We show that ultralimits of maximal representations in Sp(2n,R) admit such a framing, and that all maximal framed represen…
Maximizes coding rate difference for robust, discriminative features.
problem Learning robust, discriminative features from high-dimensional data.
method Maximal Coding Rate Reduction (MCR^2) principle.
result Significantly more robust to label corruptions in classification.
Classifies homogeneous CR hypersurfaces in low dimensions with maximal symmetry.
problem Classifying CR hypersurfaces with maximal symmetry in low dimensions.
method Introduced modified CR symbols to organize local invariants, classified hypersurfaces through modified symbols, and used Lie group structures.
result Found nine model structures among locally homogeneous 2-nondegenerate hypersurfaces in C4. Study h-principles for non-integrable distributions on manifolds.
problem Existence and classification of maximally non-integrable distributions of derived length one.
method Introduced formal structures and used h-principles to discuss existence and classification.
result Discussed existence and classification of maximally non-integrable distributions of derived length one.
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for the existence of a complete uniform differential structure on a given differenti…
The aim of this work is to prove the nonexistence of complex structures over nilpotent Lie algebras of maximal class (also called filiform).
Minimal energy local systems on curves are compact components of character varieties.
problem Characterizing local systems on surfaces with minimal energy.
method Study of minimal energy local systems on surfaces of genus g with d punctures.
result Minimal energy local systems form compact components of real relative character varieties.
New algorithm for maximizing submodular functions in real-time data changes.
problem Maximizing submodular functions under dynamic constraints.
method Randomized algorithm with O(k2) amortized update time. result 4-approximate solution to submodular maximization problem.
Bayesian scores improve structure learning in probabilistic circuits.
problem Improper structure learning in probabilistic circuits based on heuristics.
method Developed Bayesian structure scores for deterministic PCs, using them in a greedy cutset algorithm.
result Effective protection against overfitting and fast, almost hyper-parameter-free structure learner.
We study some properties of transverse contact structures on small Seifert manifolds, and we apply them to the classification of tight contact structures on a family of small Seifert manifolds.
This is the written version of a talk given in Bonn on September 11th, 2001 during a workshop on "Special structures in string theory". We report on joint work in progress with George Papadopoulos aimed at classifying the maximally supersymmetric solutions of the ten- and eleven-dimensional supergravity theories with 3…
We consider a volume maximization program to construct hyperbolic structures on triangulated 3-manifolds, for which previous progress has lead to consider angle assignments which do not correspond to a hyperbolic metric on each simplex. We show that critical points of the generalized volume are associated to geometric …
The paper studies connections in superintegrable systems, revealing geometric insights.
problem Understanding non- and semi-degenerate superintegrable systems.
method Analyzes two torsion-free connections associated with superintegrable systems.
result Semi-degenerate secondary structure tensor is the Ricci curvature of a natural torsion-free connection.
It was shown by Samelson and Wang that each compact Lie group K of even dimension admits left-invariant complex structures. When K has odd dimension it admits a left-invariant CR-structure of maximal dimension. This has been proved recently by Charbonnel and Khalgui who have also given a complete algebraic description …
We construct a partial order relation which acts on the set of 3-cliques of a maximal planar graph G and defines a unique hierarchy. We demonstrate that G is the union of a set of special subgraphs, named `bubbles', that are themselves maximal planar graphs. The graph G is retrieved by connecting these bubbles in a tre…
Investigates sequential problems on graph structures and large action spaces.
problem Sequential decision-making on graph structures and large action spaces.
method Spectral bandits, side observations, influence maximization, kernel bandits, polymatroid bandits, function optimization, infinitely many-arms bandits.
result Contributions to graph and structured bandits.
Study on a metric for disk automorphisms with maximal modulus.
problem Characterizing the metric on disk automorphisms.
method Explicit formula for the metric induced by maximal modulus.
result Characterized almost regular Finsler structure.
Maximal cusps are not dense on Teichmüller space for infinite-type surfaces.
problem Characterizing dense points in the Bers boundary of Teichmüller space for infinite-type surfaces.
method Quasiconformal deformations and analytic conditions.
result Maximal cusps cannot approach certain points on the Bers boundary.